2016 CEMC Gauss (Grade 8) Problems/Problem 7

Problem

A rectangle with a width of $2 \text{cm}$ and a length of $18 \text{cm}$ has the same area as a square with a side length of

$\textbf{(A)}\ 6 \text{cm} \qquad\textbf{(B)}\ 12 \text{cm} \qquad\textbf{(C)}\ 9 \text{cm} \qquad\textbf{(D)}\ 10 \text{cm} \qquad\textbf{(E)}\ 8 \text{cm}$

Solution

We can first find the area of the rectangle that we know the side lengths of, and then let $s$ be the side length of the square.

The area of a rectangle is its width multiplied by its length, so the area of the rectangle $2 \times 18 = 36 \text{cm}^{2}$ .

We also know that the square has the same area as the rectangle. This means that we have:

$s^{2} = 36$

Taking the square root and removing the negative solution because $s$ represents a side length, we have:

$s = \boxed {\textbf {(A) } 6 \text{cm}}$

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2016 CEMC Gauss (Grade 8) Problems/Problem 7

Problem

Solution